Photons don't have infinite energy.
JS: I don't think that Z meant that. If we naively use F/m = g with m as "inertia" then the fact that classically null geodesics have m = 0 and have g = 0 by definition, formally m is infinite if there was a finite F on the photon. This would pose problems for
E = mc^2 and the equivalence principle - and I think that was Z's point?
Of course the obvious answer to this conundrum is that F = 0 for photons and/or F = ma simply makes no sense for m = 0 particles?
On the other hand, the standard model posits m = 0 quarks and leptons prior to the Higgs mechanism and this poses a problem as Z points out.
On the other hand, leptons and quarks are micro-quantum mechanical and the classical restriction to null geodesics is not really correct because of wave-particle duality.
JW: That's just silly. When you try to push them off geodesics, they are annihilated and their finite energies are converted.
JS: What precisely do you mean here? An example? You mean when an electron absorbs a photon for example?
JW: A photon is not a non-zero restmass particle that has been accelerated to c.
JS: No one suggested it was.
JW: As for the Higgs process, it doesn't create the energy of the nonzero restmass particle produced by the interaction. It merely converts some pre-existing non zero amount of zero rest mass energy into nonzero restmass energy. The energy, before and after, has mass (given by Einstein's second law), and it is conserved. That is, the Higgs process converts, not creates. The energy, whatever its form, has mass and gravitates.
JS: I don't quite understand the above. Can you give an example? Of course, I agree that the Higgs micro-quantum mechanism should not locally violate long time on-mass-shell energy conservation (time translation invariance via Noether's theorem) - unless there are strong micro-gravity effects without a timelike Killing vector field that might describe virtual off-mass-shell processes with temporary violation of 4-momenta conservation restored in the long run in the sense of S-Matrix asymptotics of in and out states and all that stuff that 't Hooft loves. ;-)
For example in the U1 superconducting version of the Higgs mechanism
This is a harmonic oscillator with frequency ~ |?|2 (=?2) is the density of the condensate of superconducting particles.
that is, the frame-invariant mass given to the photon inside the superconductor is proportional to the ground state macro-quantum coherent order parameter. Similarly for fermions in SU2 theory there are the Yukawa couplings.
JW: Gravity, through E = m phi, cannot be the Higgs field as the Higgs field does not act on everything as gravity does.
JS: Fine, I never seriously thought it was. However, for reasons I have given I do not think there is any deep theoretical justification for phi nor is there any way to locally measure it. If I am wrong please show details. Appealing to the Schwarzschild metric is not correct in my opinion since
g00 = 1 - 2(Hubble Radius)/r
is not a good cosmological model.
that metric is only good for
2(Hubble Radius)/r < 1
outside the universe so to speak
Indeed, a better approximation for our FUTURE universe, though not our PAST early universe is
g00 = 1 - r^2/(Hubble Radius)^2
where WE are at r = 0
r^2/(Hubble Radius)^2 < 1
both the metrics above are only for accelerating static LNIF detectors held at fixed r on timelike non-geodesics by non-gravity forces.
Indeed their local proper accelerations stuck in curved spacetime are
g(r) = (Newton's g)/[g00(r)]^1/2
they see Unruh black body radiation at temperature
T(r) = hg(r)/ckB